Practical aspects of higher-order numerical schemes for wave propagation phenomena

This paper examines practical issues related to the use of compact-di erence-based fourth- and sixth-order schemes for wave propagation phenomena with focus on Maxwellʹs equations of electromagnetics. An out- line of the formulation and scheme optimization is followed by an assessment of the error accruing from application on stretched meshes with two approaches: transformed plane method and physical space di er- encing. In the rst technique, the truncation error expansion for the sixth-order compact scheme con rms that the order of accuracy is preserved if a consistent mesh re nement strategy is followed and further that metrics should be evaluated numerically even if analytic expressions are available. Physical space-di erencing formulas are derived for the ve-point stencil by expressing the coe cients in terms of local spacing ratios. The order of accuracy of the reconstruction operator is then veri ed with a numerical experiment on stretched meshes. To ensure stability for a broad range of problems, Fourier analysis is employed to develop a single-parameter family of up to tenth-order tridiagonal-based spatial lters. The implementation of these l- ters is discussed in terms of their e ect on the interior scheme as well as in a 1-D cavity where they are employed to suppress a late-time instability. The paper concludes after demonstrating the application of the scheme to several 3-D canonical problems utilizing Cartesian as well as curvilinear meshes. Published in 1999 by John Wiley & Sons, Ltd. This article is a U.S. Government work and is in the public domain in the United States.